This invention relates generally to coherent light sources. More particularly, it relates to high power optical fiber lasers with doping profiles selected to produce complex-valued Vc-parameters to support gain-guiding of radiation.
Optical fiber lasers have a core doped with ions capable of providing laser amplification when pumped with optical energy. In conventional fiber lasers, the core has a higher index of refraction than the surrounding cladding. Fiber lasers have a number of inherent advantages compared to solid state and gas lasers. Fiber lasers are simple, rugged, and inexpensive devices with a minimum of complex-valued optical and mechanical components. Optical fiber materials are compatible with a very wide range of solid state laser ions operating at many different wavelengths. These laser ions can be distributed along a substantial length of fiber, up to many meters long, with the pumping light fully trapped within the fiber over the full distance. At the same time the unwanted optical losses for either pump or signal waves can be very small in modern fibers. For additional background information on fiber lasers the reader is referred to U.S. Pat. No. 3,808,549 to Maurer.
In many applications, both for telecommunications and for fiber laser devices, it is desirable to have a single mode fiber, i.e., a fiber that can propagate only one single lowest-order mode, with no higher-order modes being able to propagate or be trapped by the fiber. For general teaching on single-mode fiber lasers the reader is referred to Poole et al., xe2x80x9cFabrication of Low-Loss Optical Fibers Containing Rare-Earth Ionsxe2x80x9d, Optics Letters, Vol. 22, 1985, pp. 737-738. Now, specifically, achieving single-mode behavior requires a combination of a small enough index step xcex94n between the core and cladding regions of the fiber and a small enough diameter d for the core region of the fiber.
Since optical fibers have a relatively small diameter (e.g.  less than 1 mm, which is small compared to solid state lasers), the optical power densities are large even for small total optical powers. This leads to both efficient pumping and efficient signal extraction in a wide variety of laser ions. All of the incident pumping radiation can be absorbed by the laser ions even on very weakly absorbing pump transitions, and the overall conversion of pumping light to laser output can be extremely efficient. Further, the small outer diameter of the optical fiber permits efficient heat extraction.
In recent years, high power fiber lasers have been manufactured with ever increasing optical powers. A major advance has been the development of xe2x80x98cladding pumpedxe2x80x99 fiber lasers as disclosed in U.S. Pat. No. 4,815,079 to Snitzer et al. In cladding pumped fiber lasers, the laser light is confined to a small core (usually single mode) while the pump light propagates in a much larger cladding surrounding the core. The laser light in the core retains its desired single mode characteristic while the pump light is gradually absorbed by the lasing ions in the core. The large cladding permits high pump energies to be injected into the ends of the fiber, and permits this pump energy to be supplied by spatially incoherent pump sources such as spatially incoherent diode laser arrays. This increases the attainable power output of fiber lasers. Fiber lasers providing tens of watts of optical power output are now possible with cladding pumped designs. This has made possible new applications for fiber lasers including material processing and other high-power applications.
An important objective in the design of many optical fiber lasers is to obtain amplification of only a single transverse mode of the fiber core. This severely limits the size of the fiber core. The diameter of the core in conventional index-guided fibers must be limited to less than about 10 microns if the laser output is to have only a single transverse mode. Cores larger than this will propagate multiple higher-order transverse modes. This size limitation results in a ceiling on the achievable output power of the fiber laser due to a maximum power intensity that the core can carry. When the laser power intensity (watts/mm2) in a single mode fiber exceeds a certain maximum value, stimulated Raman scattering occurs which converts the laser light to other wavelengths. The Raman scattering is inherent in the fiber material itself and places an absolute limit on the maximum power intensity the core can carry. The threshold for the onset of stimulated Raman scattering is a few tens of watts for single mode cores of typical size. Increasing the size of the core reduces the power intensity, thereby preventing Raman scattering, but invariably allows unwanted high-order transverse modes to be produced.
In U.S. Pat. No. 5,818,630 Fermann et al. teach single-mode amplifiers based on multi-mode fibers. The problem of multi-mode propagation and mode conversion is partially avoided by using relatively short fiber lengths together with careful shaping or mode-matching of the injected light so as to launch only the preferred fundamental or lowest-order mode at the input end of the fiber, and with the entire length of the fiber maintained in a very straight line so as to minimize conversion of the light into higher-order modes as the light travels along the fiber. In addition, Fermann et al. teach confinement of the doping to the center of the fiber core in order to preferentially amplify the fundamental mode, to reduce amplified spontaneous emission and to allow gain-guiding of the fundamental mode, which is centered on the fiber axis. In addition, Fermann et al. propose that mode-filters be integrated into the laser cavity to promote a single near-diffraction limited mode. The fibers used by Fermann et al. have a V-parameter higher than 2.5 and a relatively high index of refraction difference between the fiber core and cladding.
The term gain-guiding as used by Fermann et al. defines a gain confinement or preferential amplification achieved by the doping profile. The fibers do not actually gain-guide any modes, rather, the modes are guided because of the refractive index profile. In other words, the doping profile does not support any guided modes.
In U.S. Pat. No. 5,712,941 to Imoto et al. teach the use of single-mode fiber with multiple cores and consolidated cores exhibiting various doping profiles. In this case the doping profiles also do not support any gain-guiding and a refractive index profile is used to define the guided modes.
In U.S. Pat. No. 5,187,759 DiGiovanni et al. teach a high gain multi-mode optical amplifier which attempts to prevent excitation of the numerous higher order modes. DiGiovanni et al. teach to carefully launch the radiation substantially along the center axis of the multi-mode fiber within a predetermined launch angle. Thus, rather than exciting all modes, only lower order modes are affected. They also teach that the doping profile can be adjusted to further reduce mode coupling.
Unfortunately, none of the above solutions can be used to produce a long and stable multi-mode fiber operating in just the fundamental mode and yielding high output power. In fact, due to optical aberrations, even well corrected optics used to carefully launch radiation into multi-mode fibers typically allow the excitation of the fundamental mode only with maximum efficiency of about 95%. Therefore, to date, it has been considered that mode-locking of a multi-mode fiber is impossible and no stable operation of a mode-locked multi-mode fiber laser has yet been demonstrated.
In U.S. Pat. No. 6,275,512 Fermann teaches a mode-locked multi-mode fiber laser pulse source and suggests that the above-mentioned problems be overcome by suitable cavity design. Specifically, Fermann teaches the use of a saturable absorber in the laser cavity to achieve mode locking in multi-mode fibers. His objective is to achieve stable generation of high peak power pulses from mode-locked multi-mode fibers. Unfortunately, such mode locking cannot be easily employed and can lead to damage of the absorber when high peak powers are reached.
Therefore, the problem of producing a fiber laser which has a large core diameter but guides only the lowest order mode, or a select number of lower order modes and produces high output power remains. Specifically, it would be an advance in the art to provide a fiber laser with a large core cross-section that is relatively long, produces output power in the kilowatt range and only guides the fundamental mode or a select number of lower order modes.
Accordingly, it is a primary object of the present invention to provide an optical fiber that can be used in a fiber laser to produce output in a single mode or a minimal number of low-order modes. It is a further object of the invention to ensure that the optical fiber laser is easy to use and provides kilowatt level power. These and other objects and advantages will be apparent upon reading the following description and accompanying drawings.
These objects and advantages are attained by an optical fiber with a complex-valued Vc-parameter. The optical fiber has a core, a cladding surrounding the core and an active dopant distributed in the optical fiber in accordance with a doping profile. The doping profile establishes a gain g that makes a sufficiently large contribution to an imaginary part of the complex-valued Vc-parameter to define at least one gain-guided mode, e.g., the fundamental mode or several low-order modes of a radiation in the optical fiber. In other words, the imaginary part of the Vc-parameter defines the gain-guiding properties of the optical fiber.
The core and the cladding can also be designed to exhibit a refractive index profile. The refractive index profile and the gain profile then jointly contribute to the complex-valued Vc parameter of the fiber, and together determine the modes and mode propagation properties of the fiber.
As will be demonstrated in the following, in fibers with complex-valued Vc-parameters it is generally more convenient to characterize these fibers not by the complex value of the Vc parameter itself, but by the square of this value, that is, by the value of the square of the complex-valued Vc-parameter. In this convention gain g in the fiber contributes to the imaginary part of the square of the complex-valued Vc-parameter, while the refractive index profile (if present) contributes to the real part of the square of the complex-valued Vc-parameter. It is important to note that in accordance with the present invention it is not necessary that the fiber have an index profile accompanying the gain g for the fiber to guide gain-guided modes. A purely gain-guided fiber with no index profile will have a purely imaginary value of the square of the complex-valued Vc-parameter, with the real part of the square of the complex-valued Vc-parameter being zero.
In one embodiment the real part contributed to the square of the complex-valued Vc-parameter due to the index profile is positive. The actual index profile can be of any suitable shape including graded-index profiles, W-, M- and other more complex-valued profiles. In one embodiment the index profile is a step-profile, e.g., with the core having a higher index n, and the cladding having a lower index no. In this case the optical fiber exhibits index-guiding of the radiation in addition to gain-guiding. In another embodiment, the index profile can be such that the real part is negative. In this case the index-profile can also be of any suitable shape including graded index profiles, W-, M- and other more complex-valued profiles. In one embodiment, the index profile is a step-profile, e.g., with the core having a lower index and the cladding having a higher index. When the real part of the square of the complex-valued Vc-parameter is negative the optical fiber exhibits index-antiguiding in addition to gain-guiding.
The optical fiber of the invention can be a single-mode fiber or a multi-mode fiber. It is important to bear in mind, that the gain-guiding contribution to the complex-valued Vc-parameter will allow the designer to obtain a fiber with a larger core diameter which will still support a single mode or a few low-order modes of radiation. It is particularly useful to build fibers with core diameters in the range of 50-500 microns.
The optical fiber has a fiber axis passing through its core. Depending on the modes that are gain-guided, the doping profile can have a maximum on the fiber axis. For example, the doping profile can have a maximum on the fiber axis and decrease monotonically with increasing fiber radius. For example, the doping profile can be parabolic and centered on the fiber axis. In yet another embodiment, the doping profile can have a step-profile with one or more steps. A person skilled in the art will recognize that many other doping profiles are possible. The active dopant preferably includes active ions such as Nd, Yb, Er or other suitable lasant materials.
The optical fiber of the invention is preferably used as a fiber laser or as a laser amplifier. When used in these capacities it is convenient to pump the optical fiber through its cladding. A pump source coupled to the cladding provides the requisite pump radiation that passes into the core to stimulate the active dopant, i.e., the ions of Nd, Yb, Er or others.
The invention also provides a method for designing an optical fiber with a complex-valued VC-parameter. In accordance with the method the core and cladding surrounding the core are defined. The optical fiber is doped with the active dopant such as active ions of Nd, Yb, Er or others to produce a certain doping profile. The doping profile establishes a gain g inside the optical fiber that makes a sufficiently large contribution to the imaginary part of the complex-valued VC-parameter to define at least one gain-guided mode of radiation within the fiber. The method of the invention can be extended to further defining an index profile that establishes index-guiding or index-antiguiding. It is also possible to use no index effects at all. When working with step profiles, i.e., when the index exhibits a step index profile and the dopant exhibits a step dopant profile it is convenient to approximate the complex-valued said complex-valued VC-parameter as:             V      c        ≈                  (                              2            ⁢            π            ⁢                          xe2x80x83                        ⁢            a                    λ                )            ⁢                        2          ⁢                                    n              1                        ⁡                          [                                                Δ                  ⁢                                      xe2x80x83                                    ⁢                  n                                +                                  j                  ⁢                                      xe2x80x83                                    ⁢                                      λ                                          2                      ⁢                      π                                                        ⁢                  g                                            ]                                            ,
where a is the core radius, xcex94n is the index difference between the core and cladding, and xcex is the free space wavelength of the radiation. As noted above, it is convenient to consider instead the square of the complex-valued VC-parameter:             V      c      2        =                            (                                    2              ⁢              π              ⁢                              xe2x80x83                            ⁢              a                        λ                    )                2            ⁢      2      ⁢                        n          1                ⁡                  [                                    Δ              ⁢                              xe2x80x83                            ⁢              n                        +                          j              ⁢                              xe2x80x83                            ⁢                                                λ                  ⁢                                      xe2x80x83                                    ⁢                  g                                                  2                  ⁢                  π                                                              ]                      ,
since it is then apparent that the index difference xcex94n is entirely responsible for the real part of the square of the complex-valued VC-parameter, while the gain profile g is entirely associated with the imaginary part of the square of the VC-parameter. Further details of the invention are explained in the below detailed description with reference to the attached drawing figures.